Mr Wilkie has questioned Opposition leader Tony Abbott's judgment in making the offer of money to rebuild the Royal Hobart Hospital, describing it as "almost reckless".
Mr Wilkie on Thursday announced he would support Prime Minister Julia Gillard's attempt to form a government because he believed Labor would better be able to offer a stable, competent and ethical government.
Mr Wilkie said he had rejected Mr Abbott's offer of the cash because he thought it was "almost reckless" and because Mr Abbott had not explained where the money would come from.
He told the ABC that Mr Abbott may be regretting making his hospital offer in light of a potential $11 billion shortfall in Coalition costings.
But the Coalition disputes Mr Wilkie's version of the negotiations, saying he was the one who asked for the billion-dollar spending commitment.
Opposition Treasury spokesman Joe Hockey said Mr Wilkie never asked where the funds would come from.
Opposition finance spokesman Andrew Robb joined the attack, saying Mr Wilkie lobbied hard for substantial funds for the hospital, the ABC reports
Mr Wilkie has agreed to support Labor in return for $340m for the hospital and commitments on gambling reforms.